Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks

Sjögreen, Björn; Yee, H. C.; Wray, A. A.

doi:10.1007/s00193-019-00925-z

Cited by 4 publications

(3 citation statements)

References 33 publications

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“…The basic idea of these schemes is to use a high-dissipative shock-capturing scheme near a shock-wave and a lowdissipative upwind scheme or none-dissipative central scheme in the smooth region. Examples of such a scheme are the hybrid upwind/WENO schemes [68][69][70][71][72], and the hybrid central/shock-capturing schemes [73][74][75]. A shock sensor is essential for a hybrid scheme to distinguish the flow field between smooth and non-smooth parts.…”

Section: A Hybrid Scheme For Hypersonic Blunt Body Flowmentioning

confidence: 99%

A High-Order Hybrid Numerical Scheme for Hypersonic Flow Over A Blunt Body

Chen

Fang

Moulinec

et al. 2022

Flow Turbulence Combust

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A hybrid scheme is developed for direct numerical simulations of hypersonic flows over a blunt body. The scheme switches to the first-order AUSMPW+ scheme near the bow shock to provide sufficient dissipation to handle the carbuncle phenomenon. In the smooth part of the computational domain, a sixth-order central scheme with an eighth-order low-pass filter is adopted to provide high spatial accuracy to resolve turbulence. The hybrid scheme is shown to be able to obtain smooth and accurate predictions of laminar hypersonic flows over a blunt body. Using the hybrid scheme, a direct numerical simulation of a Mach 6 hypersonic flow over a circular cylinder is conducted. The result shows the turbulent structures in the near-wall region are well resolved by the hybrid scheme, and the bow shock is also captured without introducing any numerical oscillations. With the boundary layer transition on the cylinder's surface, the simulation indicates that the heat flux peak shifts from the stagnation point to the transitional zone and its peak value is increased by 50%.

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Section: A Hybrid Scheme For Hypersonic Blunt Body Flowmentioning

confidence: 99%

A High-Order Hybrid Numerical Scheme for Hypersonic Flow Over A Blunt Body

Chen

Fang

Moulinec

et al. 2022

Flow Turbulence Combust

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“…An interesting question is, if we can make use of the different (aliasing) errors in the two forms and find combinations via the split formulation where these errors cancel. We note that the idea of split formulations was already introduced in the spectral community to develop stable numerical methods for the incompressible Navier-Stokes equations e.g., [133], but is especially prominent in the finite difference fluid dynamics community e.g., [134][135][136][137][138][139]. Split formulations are used as a built-in dealiasing mechanism to stabilize numerical methods e.g., [140].…”

Section: On the Conservative Form Split Forms And Skew-symmetrymentioning

confidence: 99%

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

Gassner

Winters

2021

Front. Phys.

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In this paper we will review a recent emerging paradigm shift in the construction and analysis of high order Discontinuous Galerkin methods applied to approximate solutions of hyperbolic or mixed hyperbolic-parabolic partial differential equations (PDEs) in computational physics. There is a long history using DG methods to approximate the solution of partial differential equations in computational physics with successful applications in linear wave propagation, like those governed by Maxwell’s equations, incompressible and compressible fluid and plasma dynamics governed by the Navier-Stokes and the Magnetohydrodynamics equations, or as a solver for ordinary differential equations (ODEs), e.g., in structural mechanics. The DG method amalgamates ideas from several existing methods such as the Finite Element Galerkin method (FEM) and the Finite Volume method (FVM) and is specifically applied to problems with advection dominated properties, such as fast moving fluids or wave propagation. In the numerics community, DG methods are infamous for being computationally complex and, due to their high order nature, as having issues with robustness, i.e., these methods are sometimes prone to crashing easily. In this article we will focus on efficient nodal versions of the DG scheme and present recent ideas to restore its robustness, its connections to and influence by other sectors of the numerical community, such as the finite difference community, and further discuss this young, but rapidly developing research topic by highlighting the main contributions and a closing discussion about possible next lines of research.

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“…The blending approach of the abovementioned upwind/central-WENO hybrid schemes requires a great care to ensure numerical conservation and stability at the interface of different schemes used. Non-linear filter schemes [28][29][30][31] are developed to avoid this interface deficiency of high-order hybrid schemes. Specifically, a hybrid scheme is applied to the inviscid fluxes and the nonlinear fluxes are typically evaluated by central discretization of an entropy conservative formulation.…”

Section: Introductionmentioning

confidence: 99%

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

Hamzehloo

Lusher

Laizet

et al. 2020

Numerical Methods in Fluids

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High-speed compressible turbulent flows typically contain discontinuities and have been widely modeled using Weighted Essentially Non-Oscillatory (WENO) schemes due to their high-order accuracy and sharp shock capturing capability. However, such schemes may damp the small scales of turbulence and result in inaccurate solutions in the context of turbulence-resolving simulations. In this connection, the recently developed Targeted Essentially Non-Oscillatory (TENO) schemes, including adaptive variants, may offer significant improvements. The present study aims to quantify the potential of these new schemes for a fully turbulent supersonic flow. Specifically, DNS of a compressible turbulent channel flow with M = 1.5 and Re τ = 222 is conducted using OpenSBLI, a high-order finite difference computational fluid dynamics framework. This flow configuration is chosen to decouple the effect of flow discontinuities and turbulence and focus on the capability of the aforementioned high-order schemes to resolve turbulent structures. The effect of the spatial resolution in different directions and coarse grid implicit LES are also evaluated against the WALE LES model. The TENO schemes are found to exhibit significant performance improvements over the WENO schemes in terms of the accuracy of the statistics and the resolution of the three-dimensional vortical structures. The sixth-order adaptive TENO scheme is found to produce comparable results to those obtained with nondissipative fourth-and sixth-order central schemes and reference data obtained with spectral methods. Although the most computationally expensive scheme, it is shown that this adaptive scheme can produce satisfactory results if used as an implicit LES model.

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Skew-symmetric splitting of high-order central schemes with nonlinear filters for computational aeroacoustics turbulence with shocks

Cited by 4 publications

References 33 publications

A High-Order Hybrid Numerical Scheme for Hypersonic Flow Over A Blunt Body

A High-Order Hybrid Numerical Scheme for Hypersonic Flow Over A Blunt Body

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

On the performance of WENO/TENO schemes to resolve turbulence in DNS/LES of high‐speed compressible flows

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